The 80/20 Rule: Corporate Support forInnovation by Employees∗

Silvana Krasteva† Priyanka Sharma‡ Liad Wagman§

May 19, 2014

Abstract

We model an employee’s decision to pursue an innovative idea at his em-ploying firm (internally) or via a start-up (externally). We characterize an ideaby its market profitability and the degree of positive/negative externality thatit imposes on the employing firm’s profits. The innovation process consistsof exploration and development. Exploring an idea internally grants the em-ployee access to exploration support from the firm, but reduces his appropri-ability of the idea. We demonstrate that ideas exhibiting weak externalitiesare explored and developed externally whereas ideas with strong externali-ties are explored and developed internally. Moderate externalities are associ-ated with internal exploration, but subsequent external development. An in-crease in the firm’s exploration support attracts internal exploration of a widerrange of ideas, but increases the likelihood of subsequent external develop-ment. Moreover, the firm’s exploration support and profitability respond non-monotonically to policies that improve its appropriability of new ideas.

Keywords: Innovation, R&D, Entrepreneurship, Exploration support.JEL Codes: O31, O34, L51.

∗We wish to thank participants at the Texas A&M theory workshops, the Illinois Institute ofTechnology Stuart School of Business seminar series, participants at the Summer Meetings of theEconometric Society, the Texas Economic Theory Conference, INFORMS, and participants at the In-ternational Industrial Organization Conference for their helpful feedback and suggestions. We areextremely grateful to Stephanie Houghton, Arvind Mahajan, Guoqiang Tian, and Thomas Wisemanfor their useful comments.

†Department of Economics, Texas A&M University. Email: ssk8@tamu.edu.‡Stuart School of Business, Illinois Institute of Technology. Email: psharm21@stuart.iit.edu.§Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern

University. Email: l-wagman@kellogg.northwestern.edu.

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1 Introduction

Evidence indicates that innovations developed by start-ups are often conceived byformer employees of established firms who undertake projects that had been over-looked by their employers. These innovations are frequently related to the respec-tive parent firms’ lines of business (Bhide, 1994; Agarwal et al., 2004; Klepper andSleeper, 2005; Franco and Filson, 2006; Cassiman and Ueda, 2006). For instance,FriendFeed, Aardvark, and Nextstop were founded by former Google employees,with each closely connected to their founders’ work at Google.1 Similarly, formerMicrosoft employees Rob Glaser, Gabe Newell, and Rich Barton famously went onto found RealNetworks, Valve, and Zillow, each directly connected to their pastresponsibilities at Microsoft (Rich Barton also co-founded Expedia.com as part ofhis employment at Microsoft in 1994; it was later spun off).

While innovations may eventually be developed outside of their respective par-ent firms, the initial exploration often occurs within. In fact, many of the firmsthat bear a reputation for employees leaving to form start-ups, including Amazon,Google, and Microsoft, also have in place generous policies for supporting explo-ration of new ideas. Firms such Chubb,2 LinkedIn,3 and Apple4 followed Googlein implementing generous company policies for allowing employees to explorenew ideas “on the company’s dime.” Google’s renowned 80/20 “Innovation TimeOff” (ITO) policy encourages employees to take 20 percent of their time to workon company-related projects of their choosing. The policy has led to some excep-tionally successful commercial products, including Gmail, AdSense, and GoogleNews, and in-house utility tools like Google Moderator.5

A firm’s choice to support exploration of new ideas by its employees, in lieu ofnegotiating exploration-contingent contracts, can be understood in light of the na-ture of the innovation process. Innovative ideas are frequently the result of unpre-dictable and non-contractible initiatives, which go beyond employees’ normallyprescribed tasks (Aghion and Tirole, 1994; Hellmann and Thiele, 2011). Thus, in-

1Numerous other start-ups that bear a relationship to Google’s product line were founded byformer Google employees, including Ooyala, Dasient, TellApart, Cuil, Redbeacon, Mixer Labs,Howcast, MyLikes, Weatherbill, Doapp, reMail, Hawthorne Labs, and AppJet, among others.

2http://sloanreview.mit.edu/article/redesigning-innovation-at-chubb/3http://www.wired.com/2012/12/llinkedin-20-percent-time/4http://goo.gl/42rer75http://goo.gl/CJq38

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centive contracts based on measurable performance objectives studied in the liter-ature (e.g., Holmstrom, 1991; Holmstrom and Milgrom, 1991, 1994; Gibbons, 1998)are often hard to structure and evaluate in practice. Policies for corporate inno-vation, such as Google’s ITO policy, have attracted considerable media and prac-titioners’ attention in recent years,6 and their profitability has been questioned.7

This paper aims to gain a better understanding of the relationship between a firm’ssupport for innovation and employees’ choice of whether to innovate and whereto pursue new ideas.

We present an integrated model that incorporates both the firm’s problem ofincentivizing innovation by its employees as well as an employee’s choice of pur-suing an innovation internally or externally. Similar to Pakes and Nitzan (1983),a new idea in our framework can be turned into a marketable innovation in twostages — exploration and development. Exploration turns a non-verifiable andnon-contractible idea into a working prototype that can be evaluated by a thirdparty, while the development stage turns the prototype into a marketable product.

From the employee’s perspective, external exploration has the advantage ofa higher appropriability of the innovation. The benefit of internal exploration istwofold. First, the employee can take advantage of the firm’s exploration support,which may increase the likelihood of successful exploration. Second, internal ex-ploration and handling of an idea may be more efficient if the idea is related tothe firm’s line of business (e.g., due to better tailoring of new products to existingones). Given the trade-offs that the employee faces upon coming up with an idea,he chooses whether to ignore the idea and focus on other (core) tasks, explore theidea internally, or explore the idea externally. Our objective is to understand howthe firm’s level of support and the conceived idea’s characteristics interact with theemployee’s exploration and retention incentives.

Our model gives rise to the prediction that at the early exploration stage, firmstend to bleed out ideas that impose weak (positive or negative) externalities on ex-isting profits, and retain ideas with strong externalities. This is primarily becauseideas exhibiting stronger externalities are associated with higher efficiency gainsfrom joint development. This prediction is consistent with some empirical evi-dence. In particular, in the semiconductor, laser and disk-drive industries, spinoffsare likely to enter new niche markets that do not significantly affect the profits of

6http://www.forbes.com/innovative-companies/.7http://blogs.hbr.org/cs/2010/08/free_time_innovation.html

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parent firms (Christensen, 1993; Klepper and Sleeper, 2005; Klepper, 2010).Our model also incorporates heterogeneity in terms of employees’ potential for

entrepreneurship (e.g., due to varying abilities and access to capital), where an em-ployee’s type is private information and affects his profitability from the externalpursuit of an idea. Allowing for this heterogeneity leads to interesting dynamicsin the downstream once an innovation has been explored; that is, once a proto-type has been completed. In particular, in the development stage, disagreementsbetween the firm and the employee regarding the division of proceeds from aninnovation may lead to the employee’s departure. These disagreements are theresult of the firm’s inability to observe the employee’s type. Our model gives riseto the prediction that internal exploration and subsequent external developmentoccurs for ideas exhibiting moderate externalities. Employees take advantage ofthe firm’s resources in exploring such ideas, but may later find the downstreamcompensation insufficient for internal development, leading to departures.

In equilibrium, since low-type employees have less attractive outside options,and consequently weaker incentives to pursue ideas externally, their initial explo-ration decision may signal their types. Interestingly, as the firm increases its sup-port for exploration, the firm’s ability to infer an employee’s type diminishes —as all employee types find internal exploration more attractive. Therefore, whileincreasing its exploration support helps the firm attract more ideas for internal ex-ploration, it can also give rise to more downstream disagreements, as the firm findsit increasingly difficult to evaluate an employee’s outside option. This finding isconsistent with the anecdotal evidence mentioned above, where firms which aremost supportive of employees’ exploration, such as Google and Amazon, are alsorenowned for having employees leave to form new ventures.

Thus, aside from the inherent costs associated with supporting innovation,firms face additional important trade-offs in determining their levels of support.In particular, a firm’s exploration support may not only grant the firm access tonew ideas, but can also facilitate a screening mechanism that enables employeesto signal their types. This type of signaling can help firms retain more ideas in-ternally at their development stage, and by doing so, realize efficiencies from jointdevelopment with their original employee innovators.

How, then, does a firm’s optimal choice of support and its expected profit in-teract with its ability to appropriate innovation proceeds? A firm’s degree of ap-propriability is affected by numerous factors such as the innovating employee’s

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indispensability in the development process, the firm’s control over vital produc-tion inputs, intangible benefits received by the employee from external develop-ment, and the employee’s potential for independent development. We show thatif a firm is seeking to attract a wide spectrum of employee types, then its optimallevel of support is positively related to its degree of appropriability. That is, asits shares of the proceeds from new product innovations rise, so does its optimallevel of support. The reason for this is intuitive. First, the increase in the firm’sdownstream profits from new ideas makes internal exploration more attractive forthe firm. Second, since employees anticipate less favorable contractual terms inthe downstream, they are less willing to explore new ideas in-house —unless thefirm increases its level of support.

However, a higher degree of appropriability does not necessarily benefit thefirm — and may in fact reduce its expected profit. This is because the cost ofmaintaining the flow of ideas brought internally can outweigh the gains from ap-propriating larger proceeds in the downstream. Furthermore, for high degrees ofappropriability, the firm may find it too costly to retain ideas from high-type em-ployees, leading to a substantial decrease in its level of exploration support. Thesefindings give rise to the following empirical implication: Industries where firms’appropriability of employees’ ideas is significant (e.g., due to high levels of intel-lectual property protection and/or enforceability of non-compete agreements), arealso likely to be characterized by firms offering less support for innovation.

2 Related Literature

There is a significant body of literature that addresses different aspects of inno-vation in firms. The questions related to the employee’s incentives to leave es-tablished companies to form start-ups (e.g., Pakes and Nitzan, 1983; Anton andYao, 1995; Amador and Landier, 2003; Klepper and Sleeper, 2005; Cassiman andUeda, 2006; Hellmann, 2007; Thompson and Chen, 2011) and inducing innovationwithin firms (e.g., Holmstrom, 1989; Holmstrom and Milgrom, 1991; Aghion andTirole, 1994; Inderst and Klein, 2007; Bernardo et al., 2009; Hellmann and Thiele,2011; Manso, 2011) have been at the forefront of the entrepreneurship literature.Interestingly, the analysis of these two important aspects of innovation in firms —inducing innovation and new venture formation — has been largely disconnected.

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We bridge this gap by studying the choices of (i) exploration support by the firm,and (ii) start-up formation by employees, in an integrated model.

Some of the emerging explanations for employee departure include labor mar-ket frictions (Astebro et al., 2011); information asymmetries and overly optimisticemployees (e.g., Amador and Landier, 2003; Thompson and Chen, 2011); lack ofcommitment by established firms to not expropriate innovative ideas (e.g., Pakesand Nitzan, 1983; Anton and Yao, 1994, 1995; Wiggins, 1995; Gans et al., 2002; Gansand Stern, 2003); firm’s optimal pre-commitment to reject innovation by employeesin order to incentivize effort on the firm’s core business (Hellmann, 2007); know-how acquisition by employees that increases their potential for entrepreneurship(Franco and Filson, 2006); inability of the established firm to prevent the devel-opment of profit-eroding innovations (Klepper and Sleeper, 2005); and a limitedcapacity for internal ventures (Cassiman and Ueda, 2006).

Our paper is closest to the literature that models start-up formation as the re-sult of informational asymmetries, including the firm’s limited information aboutthe characteristics of ideas conceived by its employees (e.g., Thompson and Chen,2011). In line with the empirical evidence (e.g., Agarwal et al., 2004; Franco and Fil-son, 2006; Klepper, 2009), we allow for new ideas to interact with a firm’s existingline of business — by either complementing or competing with the firm’s existingofferings. This is an important aspect of our model that distinguishes our workfrom much of the existing literature. It allows us to characterize an employee’sdeparture as a function of the employee’s entrepreneurial ability, the market prof-itability of an idea, as well as the degree of externality that this idea may imposeon the parent firm.

Existing literature that incorporates innovation externalities includes Gilbertand Newbery (1980), Reinganum (1983), Klepper and Sleeper (2005) and Cassimanand Ueda (2006). With the exception of Cassiman and Ueda (2006), this literaturefocuses only on innovations that cannibalize profits from existing products, whileomitting the possibility of complementary innovations. More importantly, privateagreements for joint development between potential entrants and existing firmsare ruled out. This gives rise to the prediction that entrants may have strongerincentives compared to existing firms to develop substitute ideas, which goes con-trary to our findings.

By allowing for both complementary and substitute ideas, and the possibilityof internal handling of innovations, our work is closest to Cassiman and Ueda

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(2006). However, unlike in our model, internal development in Cassiman andUeda’s model is independent of the idea’s proximity to the established firm’s lineof business. Cassiman and Ueda conjecture that the firm possesses superior com-mercialization capability, which is unaffected by the idea’s closeness to the firm’sexisting offerings. This makes the established firm more willing to develop ideaswith wider range of profitability. As a result, Cassiman and Ueda predict thatinternally-commercialized ideas are on average more cannibalizing and less prof-itable compared to externally commercialized ideas. In contrast, a defining featureof our model is the firm’s superiority in handling ideas related to the firm’s lineof business. As a result, we find that the firm retains ideas that exhibit signifi-cant negative or positive externalities, giving rise to the prediction that start-upsdevelop products that are weakly related to the parent firm’s existing offerings.This finding is more in line with the empirical regularities observed in the litera-ture (e.g., Franco and Filson, 2006; Christensen, 1993; Klepper and Sleeper, 2005;Klepper, 2010).

Our paper is also closely related to the growing literature on motivating in-novation within established firms. While much of this literature (e.g., Holm-strom, 1989; Inderst and Klein, 2007; Bernardo et al., 2009; Manso, 2011) takes amechanism-design approach of characterizing optimal innovation-inducing con-tracts, some papers (e.g., Aghion and Tirole, 1994; Hellmann and Thiele, 2011)characterize innovation activity as unplanned, non-contractible, and not subject tothe standard incentive contract. The closest paper to ours on this topic is Hellmannand Thiele (2011), who consider a multitask incentive problem with one plannedcontractible activity (the standard, core task) and one unplanned non-contractibleactivity (innovation). A defining feature of their model is the mutual exclusivenessof the two activities, which allows for the contractual terms of the planned activityto influence an employee’s non-contractual innovation incentives. In contrast, ourmulti-tasking model allows for co-existence of the two activities. Our focus is onhow a firm’s unconditional policy to support exploration, along the lines of poli-cies championed by Google, interacts with an employees’ choice of whether andhow to explore innovative ideas.

The remainder of the paper is organized as follows. Section 3 formally sets upthe model. Section 4 consists of equilibrium analysis with the following subsec-tions: 4.1 and 4.2 solve for the expected payoffs from internal exploration and char-acterize an employee’s optimal exploration strategy; 4.3 addresses the employee’s

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development strategy as a function of the firm’s exploration support; 4.4 charac-terizes the firm’s optimal level of support and derives comparative statics results.Section 5 concludes. Proofs are relegated to an Appendix. For convenience, Ta-ble 1 contains a summary of the notation and is provided on the last page of theAppendix.

3 Model

The model consists of a firm (denoted by f ) and a research employee (denoted bye, where we make use of the terms researcher and employee interchangeably). Theresearcher receives a competitive wage, w, to work on a “core task” assigned bythe firm. Consistent with the literature (e.g., Pakes and Nitzan, 1983; Cassimanand Ueda, 2006; Hellmann, 2007), we assume that in the course of his work, theresearcher may serendipitously come up with an innovative idea. The idea is char-acterized by two components: (i) market profitability, vi, and (ii) an externality,∆, that is imposed on the firm’s existing profit. The market profitability is drawnfrom a Bernoulli distribution taking a high value vi = v with probability ψ and alow value vi = 0 with probability 1− ψ. The externality imposed on the firm isdrawn from a conditional distribution F(∆|vi) with support [∆, ∆], where ∆ < 0and ∆ > 0, allowing for both positive and negative externalities (complementaryand substitute ideas, respectively). Moreover, the general specification of F(∆|vi)

allows us to capture possible correlation between market profitability and the ex-ternality to the firm.8

The innovation process consists of two stages: exploration and development.At the exploration stage, the employee privately observes (vi, ∆). The probabil-ity of successful exploration is given by p(L), where L denotes the pre-committedexploration support by the firm on the likelihood of successful exploration. Weassume that p′(L) > 0 and p′′(L) ≤ 0, reflecting the positive and diminishing ef-fect of L. External exploration succeeds with probability po. Successful explorationresults in a working prototype. If exploration takes place internally, the character-istics of the prototype are also observed by the firm. The subsequent development

8For instance, a close substitute to the firm’s existing products is likely to exhibit both highnegative externality to the firm as well as low market profitability as market competition erodesprofits. The relationship between market value and the degree of externality to the firm is less clearfor complementary products.

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Firm chooses support for internal innovation L

Employee comes up with an idea

Explore externally

Develop externally

po

(πEf , πE

e )

Remain with the firm

Drop the idea

(−L, w)

Explore internally

Negotiate over surplus

p(L) 1 − p(L)

Agreements to split π J Disagreements result in πof and πo

e

1

Figure 1: Timing of the game.

stage transforms a prototype into a marketable product. In either stage, the em-ployee may choose to leave the firm to independently pursue the innovation.

The timing of the game is illustrated in Figure 1. At the onset, the firm choosesits level of exploration support L. Upon coming up with an idea for an innovation,the employee can choose to (1) remain within the firm (denoted by R) and exploreinternally or drop the idea and work on his core task for the wage w; or (2) explorehis idea externally (denoted by E).9

Successful external exploration results in a prototype with market profitabilityvi. The extent to which the employee appropriates this value externally dependson his privately known type, β, which reflects the subsequent share of start-upproceeds retained by the employee. We allow for high (βH) and low (βL) types,with 1 ≥ βH > βL ≥ 0, and a prior Pr{β = βH} = θ ∈ (0, 1). Therefore, givenan externality of level ∆, the respective expected payoffs for the employee and thefirm from external exploration are πE

e (vi, β) = poβvi and πEf (vi, ∆) = po∆1(vi =

9It is possible that the firm’s support can also provide the employee with benefits that can beused by non-innovating employees. For instance, the employee may use ”Innovation Time Off”support for leisure purposes. Our model can be easily extended to incorporate such additionalbenefits of the firm’s support. However, since an increase in the base wage would have the sameimpact in our model, we focus only on the type of exploration support that affects the incentivesfor internal exploration.

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v), where 1(·) denotes the indicator function.Successful internal exploration reveals the characteristics of an idea, (vi, ∆), to

the firm and allows it to gain some control over its intellectual property.10 Con-sequently, the firm and the employee negotiate over the division of potential pro-ceeds from the development stage. The outcome of this negotiation depends bothon the surplus from joint development and on the two parties’ outside options.

The surplus from joint development is denoted by π J(vi, ∆) = max{g∆+ vi, 0},where the parameter g captures any efficiencies from joint development (withgs < 1 for substitutes and gc > 1 for complements) resulting from the efficientmanagement of the externality ∆. Such synergies may be due to reduced competi-tive pressure or superior technological and commercialization ability of the firm tobetter position the new product with the firm’s existing offerings. 11 Thus, internaldevelopment results in the highest surplus.

The disagreement payoffs of the employee and the firm in the developmentstage are given by πo

e (vi, β) = βαevi and πof (vi, ∆) = (α f vi + ∆)1(vi = v) +

max{0, ∆}1(vi = 0). The parameters αe and α f , which denote respective resultantmarket shares for the employee and the firm, are assumed to be common knowl-edge. To incorporate the profit-eroding effects of possible competition or property-rights disputes between the firm and the employee, we assume αe + α f ≤ 1. Forlow-profitability ideas, we have πo

e (vi = 0, β) < w. Henceforth, we assume that forhigh-profitability ideas, πo

e (vi = v, β) ≥ w holds, making external development acredible outside option for the employee.

Disagreements over the joint development of an innovation may arise in equi-librium due to the unobservability of the employee’s type. The negotiation stageis modeled as a random-proposer bargaining game, with γ denoting the probabil-ity that the firm makes a take-it-or-leave-it offer. The parameter γ captures factorsthat would interact with the firm’s relative bargaining position, such as corporatepolicies the firm has put in place for tracking the exploration of new ideas and de-fending its intellectual property, contractual policies for allocating proceeds from

10Internal exploration may allow the firm to gain access to the know-how from the explorationstage and establish an intellectual property claim over the idea.

11For explicit treatment of externality management through integration see Economides and Sa-lop (1992). A defining feature of integration is the integrated firm’s internalization of externalitieswhen making output decisions. This results in reducing the negative externality stemming fromsubstitutes and enhancing the positive externality stemming from complements. We capture thiseffect in a reduced form though the parameter g.

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innovations, and factors pertaining to the firm’s organizational structure (for in-stance, hierarchical vs. flat).

Remarks: The absence of exploration-contingent contracts in our model is con-sistent with common corporate policies, such as Innovation-Time-Off, and reflectsthe difficulty of structuring and enforcing contingent contracts as they pertain toinnovation. We focus on unconditional corporate exploration support as a pri-mary mechanism affecting employees’ exploration choice. While other mecha-nisms, such as varying the wage compensation for the core task, may also serveas an instrument to impact employees’ exploration choices, extending the modelin this dimension brings no added qualitative benefits.12 The assumption of acommon belief about the likelihood of the researcher’s exploration success, cou-pled with an informational advantage by the researcher pertaining to his type, canbe explained with the different set of skills required for successful research andcommercialization. While the employee’s research skills may be revealed in thecourse of his employment, his ability to successfully manage an external venturemay be more difficult to observe.13 Our approach to modeling the effect of the em-ployee’s type on his outside option is consistent with a well-functioning market,where successfully prototyped valuable ideas realize their market value — but theextent to which the researcher appropriates this value is affected by his type (e.g.,entrepreneurial ability and/or accessibility to human capital via, for example, theemployee’s “network,” and accessibility to financing). For instance, a researcherwith costlier access to financing may be inclined to surrender a larger equity staketo a venture capitalist; similarly, a researcher who lacks entrepreneurial skills mayneed to partner with additional co-founders, increasing dilution.

12A higher base wage for the employee can reduce both external exploration and developmentby the employee and has similar a effect to a higher level of support. Allowing for both instrumentswould result in similar qualitative insights as long as high-value ideas and high-type employeesare sufficiently scarce. This is because it would be too costly for the firm to fully prevent employeedeparture.

13Our model assumes that the value of the employee’s idea and his type are independent. How-ever, the model can easily account for correlation, as long as it is not perfect. The reason is that insuch cases, there will be residual uncertainty regarding the employee’s outside option, giving riseto disagreements that are analogous to our setting.

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4 Equilibrium characterization

We solve for the Perfect-Bayesian equilibrium of the game. We begin by examiningthe negotiation subgame that follows the employee’s decision to explore internally.We are specifically interested in the expected payoffs for the firm and the employeegiven internal exploration. Armed with these payoffs, we next determine how thelevel of exploration support L, the employee’s type β, and the parameters of anewly conceived idea (vi, ∆), interact with the employee’s incentives for explo-ration. Then, by weighing in the costs and benefits of widening the spectrum ofideas that the firm attracts for internal exploration, we characterize the firm’s opti-mal level of exploration support and derive comparative statics.

4.1 Internal Exploration: Negotiation Subgame

In the negotiation subgame, the firm and the employee bargain over the proceedsfrom joint development of the innovation. This stage determines the extent towhich internally explored ideas are ultimately retained by the firm. We recall thatfollowing internal exploration, ideas are completely revealed to the firm; however,the employee is still privately informed about his type. Thus, disagreements mayarise if the firm fails to sufficiently compensate high-ability employees. The firm’swillingness to pay in order to retain an employee depends on the parameters ofthe idea, vi and ∆, and on the firm’s posterior belief regarding facing a high type— conditional on an internally explored idea. Let θI denote this posterior belief.We note that this belief may be different from the prior, given by θ, since the em-ployee’s choice of internal exploration may serve as a signal about his type. Thefollowing Proposition characterizes the type of ideas that may give rise to disagree-ments.

Proposition 1 There exist cutoffs ∆ds (vi, θI) and ∆d

c (vi, θI) such that disagreements occurif and only if β = βH, vi = v and ∆ ∈ (∆d

s (v, θI), ∆dc (v, θI)). Furthermore, ∆d

s (v, θI)

(∆dc (v, θI)) is increasing (decreasing) in θI and ∆d

s (v, θI) = ∆dc (v, θI) = 0 for θI ≥

(βH−βL)αe1−α f−βLαe

∈ (0, 1).

Proposition 1 states that the firm may fail to reach an agreement with a high-type employee over ideas characterized by high market values and weak relation-ships to the firm’s existing offerings. In such cases, the probability of a disagree-

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ment is given by γθI ; that is, negotiations will break down over some ideas (afraction γθI) that fall into this group.

To glean some insight into this result, let us consider the case of complemen-tary ideas. A weakly complementary idea has little interaction with the firm’sexisting profits. Consequently, the firm makes a low compensation offer of βLαevto the researcher, which is subsequently rejected if the researcher is a high type.As the externality of the idea strengthens, the firm has more to lose from failingto reach an agreement and increases its offer to βHαev, which in turn is acceptedby both high and low employee types. Furthermore, the disagreement region forcomplementary ideas, [0, ∆d

c (v, θI)], shrinks in the firm’s posterior θI . That is, as itbecomes more likely for the employee to be a high type, the firm’s expected pay-off from making a low compensation offer decreases; in turn, the firm is inducedto increase its offer over a wider range of complementary ideas, thereby reducingdisagreements.

The intuition for substitute ideas is analogous. In this case, the firm is con-cerned about losing ideas that would result in substantial profit erosion when de-veloped externally. Consequently, the firm makes high compensation offers when-ever faced with ideas that exhibit large negative externalities. As the likelihood offacing a high type increases, the firm in turn increases its offer over a wider rangeof substitute ideas.

Proposition 1 further notes that there exists a cutoff value for the firm’s pos-terior belief, θI , specified by (βH−βL)αe

1−α f−βLαe< 1, above which no ideas are lost in

the downstream. In other words, despite incomplete information about the em-ployee’s type, disagreements are avoided entirely when the firm puts sufficientweight on facing a high-type employee.

Armed with the equilibrium characterization of the negotiation subgame, wecan derive the employee’s and the firm’s expected payoffs — both of which areimportant determinants of the incentives for internal exploration and the level ofsupport offered by the firm. The following Corollary characterizes the interactionbetween these payoffs and the degree of externality imposed by an innovation, ∆.

Corollary 1 Let πNf (vi, ∆, θI) and πN

e (vi, ∆, β, θI) denote the firm’s and the employee’sex-ante expected continuation payoffs in the negotiation subgame.

1. If ∆ > 0, thendπN

f (vi,∆,θI)

d∆ > 0 and dπNe (vi,∆,β,θI)

d∆ ≥ 0 with strict inequality for

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∆ > ∆(vi) =

{0 for vi = vw

gc−1 for vi = 0

2. If ∆ < 0, then:

a) πNf (0, ∆, θI) = πN

e (0, ∆, β, θI) = 0, and

b)dπN

f (v,∆,θI)

d∆ > 0, while dπNe (v,∆,β,θI)

d∆ < 0.

Henceforth, it will be useful to define the bargaining surplus from an idea as theadditional surplus gained from joint development relative to independent pursuitsby the (now former) employee and the firm. That is, the bargaining surplus isgiven by π J − πo

f − πoe .

We observe that a consequence of Corollary 1 is that the employee and the firmboth benefit from an idea being a stronger complement. As the magnitude of theexternality of an idea rises, the bargaining surplus and the firm’s outside option πo

fboth increase, leading to an overall increase in both the firm’s and the employee’sexpected continuation payoffs.

For substitute ideas, the employee benefits from having the outside option ofpursuing an idea with a stronger negative externality, since the firm then has agreater incentive to retain the innovation. If the idea has a low market profitability,the employee no longer possesses the credible threat of independently pursuingthe idea, whereby the bargaining surplus is 0. In contrast, for high-profit ideas,external development is feasible and the bargaining surplus shrinks as ∆ increases(that is, as the externality of a substitute idea weakens), since a weaker substi-tute idea constitutes less of a threat to the firm’s existing profit. Consequently,for substitute ideas, the firm’s (employee’s) expected payoff from the negotiationsubgame is increasing (decreasing) in ∆.

To summarize, Corollary 1 highlights the observation that the employee bene-fits from ideas that impose stronger externalities on the firm. In turn, the employeerequires weaker incentives to choose to explore such ideas within the firm — anobservation that will be key in characterizing the employee’s exploration strategy.

4.2 Optimal Exploration Strategy

Upon coming up with an idea, the employee considers the level of support offeredby the firm and chooses whether to explore the idea externally (E) or remain with

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the firm (R). Recall that external exploration results in πEe (vi, β) = poβvi. Inter-

nally, the employee can either drop the idea (D), resulting in a payoff of πDe (L) =

w, or explore the idea internally (I), giving rise to a payoff π Ie(vi, ∆, β, θI , L) =

p(L)(πNe (vi, ∆, β, θI)−w)+w. The employee chooses the exploration strategy that

maximizes his expected payoff. Thus, he will choose to remain with the firm when

max{πDe (L), π I

e(vi, ∆, β, θI , L)} ≥ πEe (vi, β) (1)

We assume that the employee breaks indifferences in favor of exploring inter-nally over externally and in favor of dropping the idea over exploring.14

Consider first the case of low-profit ideas; that is, vi = 0. We observe that theemployee would not choose to pursue low-profit ideas externally since πE

e (0, β) =

0; thus the employee either chooses to drop such ideas (D) or to explore them inter-nally (I). Internal exploration occurs only if π I

e(vi, ∆, β, θI , L) > πDe (L). From the

employee’s payoffs specified above, this implies that πNe (0, ∆, θI) > w and requires

the idea to be complementary. Corollary 1 shows that πNe (0, ∆, θI) is increasing in

the degree of complementarity. Thus, for ideas with vi = 0, the employee wouldonly consider internal exploration if the ideas are sufficiently complementary, andwould drop them otherwise.

Proposition 2 Let vi = 0. Then, both employee types choose to ignore an idea if ∆ ≤ wgc−1

and explore internally otherwise.

In contrast, high-profit ideas are always profitable to explore because of our as-sumption that πo

e (v, β) > w. Thus, internal exploration occurs if π Ie(v, ∆, β, θI , L) ≥

πEe (v, β). From Corollary 1, the employee’s continuation payoff, π I

e(v, ∆, β, θI , L), isstrictly increasing in the magnitude of the externality, ∆. Thus, if π I

e(v,0, β, θI , L) ≥πE

e (v, β), then all ideas will be explored internally. Otherwise, let ∆j(L, v, β, θI)

denote the solution of

π Ie(v, ∆j, β, θI , L) = πE

e (v, β) f or j = {s, c} (2)

Because of the strict monotonicity of π Ie(v, ∆, β, θI , L) in ∆ for both comple-

ments and substitutes, there exists a unique ∆j(L, v, β, θI) for each j = {s, c}.14Such a tie breaking rule is efficient whenever exploration is associated with a non-negligible

cost. For technical simplicity and because the qualitative nature of the results is unchanged, weabstract from incorporating costly exploration.

15

Moreover, the employee prefers internal exploration for ideas with an externalitystronger than ∆j(L, v, β, θI) and prefers external exploration otherwise. The fol-lowing Proposition formalizes this observation and describes how the firm’s levelof support, L, the employee’s type, β, and the firm’s posterior, θI , interact with theemployee’s exploration strategy.

Proposition 3 Let vi = v. There exist cutoffs ∆Is(L, v, β, θI) and ∆I

c(L, v, β, θI) suchthat the employee explores internally if ∆ /∈ (∆I

s(L, v, β, θI), ∆Ic(L, v, β, θI)) and explores

externally otherwise. These cutoffs have the following properties:

(1) ∂∆Is(L,v,β,θI)

∂L > 0 for ∆Is(L, v, β, θI) < 0.

(2) ∂∆Ic(L,v,β,θI)

∂L < 0 for ∆Ic(L, v, β, θI) > 0.

(3) ∆Is(L, v, βH) and ∆I

c(L, v, βH) are independent of θI .

(4) ∆Is(L, v, βL, θI) is non-decreasing in θI and ∆I

c(L, v, βL, θI) is non-increasing in θI .

(5) ∆Is(L, v, βH) ≤ ∆I

s(L, v, βL, θI) with strict inequality for ∆Is(L, v, βH) < 0.

(6) ∆Ic(L, v, βH) ≥ ∆I

c(L, v, βL, θI) with strict inequality for ∆Ic(L, v, βH) > 0.

Proposition 3 states that the employee chooses internal exploration of high-profit ideas that are sufficiently close to the firm’s existing offerings. Properties (1)and (2) reveal the impact of increased exploration support on employee’s choice ofan exploration venue. As expected, a higher support for exploration by the firmhas a positive effect on the employee’s incentive to choose internal exploration.Thus, by increasing its support, the firm is able to attract a wider range of ideasinside the firm.

Properties (3) and (4) reveal how the employee’s exploration incentives are im-pacted by the firm’s posterior. Notice that a high-type employee’s outside optionserves as an upper bound on the firm’s offer in the negotiation stage. Thus, thehigh type’s payoff is not impacted by the firm’s belief θI . In contrast, a low-typeemployee may benefit from a higher posterior, since the firm may increase its offerin the downstream above the low type’s outside option. As a result, for higherposteriors, a low-type employee would be more likely to bring ideas in-house.

Properties (5) and (6) reveal that for any given idea, a high-type employee is lesswilling to pursue internal exploration due to his higher outside option. In turn, the

16

firm needs to provide higher-powered incentives to attract internal exploration byhigh types.

Internal exploration may also provide an opportunity for the firm to updateits prior belief regarding the employee’s type. This occurs for ideas exhibitingrelatively weak externalities since then the exploration strategies by the two typesdiverge. The following result characterizes the unique equilibrium explorationstrategies by the two employee types and the corresponding equilibrium posterior.

Proposition 4 Let vi = v. Then, for a given level of support L:

1) If ∆ /∈ (∆Is(L, v, βH), ∆I

c(L, v, βH)), then both employee types explore internallyand θ∗I = θ is the unique equilibrium belief.

2) If ∆ ∈ (∆Is(L, v, βH), ∆I

s(L, v, βL, 0)] or ∆ ∈ [∆Ic(L, v, βL, 0), ∆I

c(L, v, βH)), ahigh-type employee explores externally while a low type explores internally andθ∗I = 0 is the unique equilibrium belief.

3) If ∆ ∈ (∆Is(L, v, βL, 0), ∆I

c(L, v, βL, 0)), then both employee types explore externallyand the equilibrium is supported by θ∗I = 0.

It follows from Proposition 4 that strongly complementary and substitute ideasare explored internally by both employee types; consequently, for ideas in thisparameter range, no new information about the employee’s type is conveyed to thefirm, whereby θI = θ. Since a low type is more inclined to explore ideas internally,ideas with intermediate level of externalities would only be explored internally bylow-type employees, whereby their type is revealed to the firm. In contrast, ideasthat are weakly related to the firm’s existing offerings are explored externally byboth employee types. For ideas in this parameter range, an off-equilibrium beliefθ∗I = 0 ensures no deviation by the low type.

Combining the findings from Propositions 1-4, the model gives rise to the pre-dictions that employees who leave their employment to form start-ups pursuehigh-profit ideas that are likely to be weakly related to their firm’s existing of-ferings. Moreover, an employee may end up leaving his firm either at the initialexploration stage or prior to the downstream development stage.

The next subsection examines how the firm’s level of exploration support inter-acts with the likelihood and timing of an employee’s potential pursuit of a start-up.

17

4.3 Timing of the Researcher’s Departure

The firm’s chosen level of exploration support has a direct impact on the em-ployee’s choice of an exploration venue, where a higher level of support leads to anincrease in exploration activity within the firm. However, as pointed out by Propo-sition 1, not all internally explored ideas are subsequently retained within the firm.Building on this result, the following finding indicates that increasing the level ofsupport indeed results in the internal exploration of a wider range of ideas. How-ever, doing so may also lead to a higher rate of disagreements in the downstream,as it becomes increasingly difficult for the firm to distinguish between high- andlow-type employees.

Proposition 5 The likelihood of internal exploration is (weakly) increasing in L. For θ ≥(βH−βL)αe1−α f−βLαe

, no downstream disagreements occur. For θ < (βH−βL)αe1−α f−βLαe

, there exists a cutoff

L ≥ 0, such that for L > L, the likelihood of downstream disagreements is increasing in L.

An increase in the level of support, L, makes internal exploration more attrac-tive for both employee types. Thus, the cutoff ∆I

s(L, v, β, θ∗I ) is increasing in L andthe cutoff ∆I

c(L, v, β, θ∗I ) is decreasing in L, reducing the range of ideas exploredoutside the firm. The likelihood of downstream disagreement depends on thefirm’s ability to distinguish between the employee’s types.

Proposition 5 states that if a high-type employee is sufficiently likely (that is,θ ≥ (βH−βL)αe

1−α f−βLαe), then identifying the employee’s type is not an issue, since the firm

always finds it optimal to make a generous offer in the downstream. However, forθ < (βH−βL)αe

1−α f−βLαe, the firm may choose to make a low price offer if the idea is weakly

related to its existing offerings.Recall that disagreements can only occur for high-profit ideas. Given low levels

of support, a high-type employee leaves the firm at the exploration stage, wherebythe firm is able to perfectly screen out the employee’s type over a wide range ofideas exhibiting weak externalities, ∆ ∈ (∆I

s(L, v, βH), ∆Ic(L, v, βH)). However,

as the level of support increases, internal exploration becomes more attractiveto the high types. As a result, disagreements occur for moderate complementsand substitutes; that is, in cases where ∆ ∈ (∆d

s (v, θ), ∆Is(L, v, βH)) and where

∆ ∈ (∆Ic(L, v, βH), ∆d

c (v, θ)). Disagreements occur because the low likelihood ofa high type and the moderate externality of these ideas make it optimal for thefirm to make low offers in the negotiation subgame.

18

From the above, it follows that the firm may never be able to implement anexploration-support strategy that completely eliminates departures by its employ-ees. All else being equal, our findings predict that firms with higher levels of ex-ploration support will experience more exploration activity within the firm, butwill also be more susceptible to losing innovations in their development stage asa result of disagreements over surplus division. As previously mentioned, thisempirical prediction is consistent with anecdotal evidence from highly innovativefirms that are known both for their generous exploration support policies — andfor a relatively large number of employee departures to pursue new ventures.

4.4 Optimal Support for Exploration

Having identified the characteristics of ideas explored and/or developed insideand outside of the firm, and the corresponding timing of an employee’s departure,we now turn our focus to the firm’s choice of exploration support. At the time ofchoosing its support, the firm has incomplete information about the characteristicsof the ideas that are likely to emerge. Hence, the firm’s decision is based on its priorbeliefs about the likely characteristics of new ideas and about the distribution ofemployee types.

Our focus in this subsection is to examine policy variables that could impactthe firm’s willingness to offer support. Among the policy variables of interest arethe firm’s relative bargaining position vis-a-vis employees, captured by γ, and theparameters α f and αe, capturing relative market strengths and development ca-pabilities for the firm and employees respectively. These variables are impactedby a variety of legal and institutional factors and affect the outcomes of negoti-ations over internal handling of innovations. Some of these factors include theallocation of property rights as determined by local laws and by firm-specific legalframeworks and policies, the indispensability of the employee’s expertise in thedevelopment process, and institutional structures that help determine the firm’sand the employee’s shares of the realized surplus.

Let πRf (vi, ∆, β, L) denote the firm’s downstream payoff following a β-type em-

ployee’s decision to keep an idea with characteristics (vi, ∆) inside the firm. If theemployee explores the idea, then πR

f (vi, ∆, β, θ∗I , L) = p(L)πNf (vi, ∆, β, θ∗I ), where

πNf (vi, ∆, β, θ∗I ) denotes the firm’s expected payoff from the negotiation subgame

conditional on a β-type employee. If the employee instead chooses to ignore the

19

idea, then πRf (vi, ∆, β, L) = 0. The firm’s payoff from external exploration is given

by πEf (vi, ∆) = p0∆1(vi = v). We recall from Propositions 2 and 4 that the firm

retains ideas with externality ∆ /∈ (∆Is (L, vi, β, θ∗I ) , ∆I

c (L, vi, β, θ∗I )), where we have∆I

s (L, 0, β, θ∗I ) = ∆Ic (L, 0, β, θ∗I ) = 0 for low-profit ideas (since they are always re-

tained within the firm).Let S f (vi, ∆, β, L) = πR

f (vi, ∆, β, L)− πEf (vi, ∆) denote the firm’s retention sur-

plus. Then, the firm’s expected profit from offering a level of support L at theoutset of the game is given by

Π f (L) =

E[S f (vi, ∆, β, L) |∆ /∈ ∆Is (L, vi, β, θ∗I ) , ∆I

c (L, vi, β, θ∗I )] + E[πEf (v, ∆)]− L (3)

Hence, the firm’s expected payoff consists of the expected externality that anidea would impose on the firm, captured by E[πE

f (v, ∆)], plus the additional sur-plus generated from retaining ideas with strong externalities within the firm. Theimpact of the level of support L on the firm’s profit is given by

∂Π f (L)∂L

= E[

∂S f (vi, ∆, β, L)∂L

∣∣∣∣∆ /∈(

∆Is , ∆I

c

)]− 1 (4)

+ψE[

S f

(v, ∆I

s , β, L)

f(

∆Is |v) ∂∆I

s∂L

∣∣∣∣ v]

(5)

−ψE[

S f

(v, ∆I

c, β, L)

f(

∆Ic|v) ∂∆I

c∂L

∣∣∣∣ v]

The level of support thus has a twofold effect on the firm’s profit. The firstterm in equation (4) captures the productivity effect of L via its impact on the likeli-hood of successful exploration, p(L). The last two terms capture the retention effectof L (that is, its effect on the employee’s incentives) via its impact on the cutoffs∆I

s (L, v, β, θ∗I ) and ∆Ic (L, v, β, θ∗I ). The retention effect is positive for substitutes

(complements) as long as ∆Is (L, v, β, θ∗I ) ∈ (∆, 0) (∆I

c (L, v, β, θ∗I ) ∈ (0, ∆)).In the remainder of this subsection, we make the following technical assump-

tion on the retention effect.

Assumption 1: For j = {s, c}, d[S f

(v,∆I

j ,β,L)

f(

∆Ij |v)]

dL ≤ 0 and ∆Ij (L, v, β, θ∗I ) 6= 0.15

15Assumption 1 is a sufficient and not a necessary condition for our analytical analysis in Subsec-tion 4.4 and is made for analytical tractability. We do not impose this restriction on our proceedingnumerical simulations.

20

Assumption 1 guarantees that whenever the retention effect is positive, it isdiminishing in the firm’s level of support. Since ∆I

s (L, v, β, θ∗I ) (∆Ic (L, v, β, θ∗I )) is

increasing (decreasing) in L, it is then straightforward to verify that there exists afinite range of L for which the retention effect is positive. The following Lemmaformalizes this observation.

Lemma 1 For every vi and β, there exist Lminj (v, β) ≤ Lmax

j (v, β) ∈ [0, ∞) for j =

{s, c}, such that ∂∆Is(L,v,β,θ∗I )

∂L > 0 and ∂∆Ic(L,v,β,θ∗I )

∂L < 0 for L ∈ [Lminj (v, β), Lmax

j (v, β))

and zero otherwise, with the following properties:

1. Lminj (v, βH) ≥ Lmin

j (v, βL) ≥ 0,

2. Lmaxj (v, βH) ≥ Lmax

j (v, βL) ≥ 0.

Lemma 1 states that the retention effect is non-monotonic in L. For low levelsof support, L < Lmin

j (v, β), the retention effect is zero, since the employee alwayschooses external exploration. For high levels, L ≥ Lmin

j (v, β), the firm successfullyinduces the internal exploration of all ideas, causing the retention effect to go downto zero again. Only for intermediate levels of support does the firm have an impacton the employee’s exploration strategy. The discrete increase in the retention effectat Lmin

j (v, β) generates a local convexity of the objective function, as the marginalbenefit of L increases discretely at this point. Consequently, the objective functionspecified by equation (3) may exhibit multiple local maxima, as illustrated in thefollowing example.

Example 1 In the following example, v = 40, ψ = 0.7, ∆ = −80, ∆ = 40, λ0 = 0.2and λv = 0.5. The employee’s type is captured by βL = 0.1, βH = 0.7, and θ = 0.7. Theprobability of a successful exploration outside the firm is po = 1− e−0.4. The effect of L onthe employee is captured by p (L) = 0.1

(1− e−0.1L−0.4) and the employee’s base pay is

w = 0.3. Efficiencies from joint-development are captured by gc = 1.1 (complements) andgs = .9 (substitutes). The relative bargaining positions are given by γ = 0.4, α f = 0.5,and αe = 0.4, with Lmin

c (v, βL) = Lmins (v, βL) = Lmin

s (v, βH) = 0 and Lminc (v, βH) ≈

2. Figure 2 plots Π f (L). Note that the objective function exhibits local convexity atLmin

c (v, βH). There are two local maxima at L1 = 0 and L2 = 3.5 corresponding to onlysubstitute ideas being attracted from the high type and both types of ideas being attractedfrom the high type with positive probability. The global maximum is at L∗ = L2.

21

0 5 10 15−6

−4

−2

0

2

4

L

ΠΠ as a funtion of L for γ = 0.3

Lcmin(β

H)

Figure 2: Firm’s ex-ante expected profit as a function of the level of support.

The presence of convex regions in the objective function Π f (L) complicates ouranalysis. It gives rise to the possibility of multiple local maxima and a global max-imum that switches from one local maximum to another, as illustrated by Example3 at the end of this section. We focus our theoretical analysis on the case where thelocal maximum for the region L ≥ max{Lmin

s (v, βH), Lminc (v, βH)} is also the global

maximum. A level of support exceeding this cutoff involves internal explorationof both complementary and substitute ideas by both employee types with positiveprobabilities.16 Thus, we focus on the case in which it is optimal for the firm toattract both employee types with complementary as well as competing ideas. Thisassumption is relaxed in Example 3.

Given L∗ ≥ max{Lmins (v, βH), Lmin

c (v, βH)}, we are interested in the effect ofchanges in the relative bargaining power of the firm, γ, and in the firm’s and em-

16Our focus on the region L∗ ≥ max{Lmins (v, βH), Lmin

c (v, βH)} is for expositional ease. Ouranalysis readily extends to the more general case where the global maximum does not switch fromone local maximum to another. In the context of our model, this implies that if the firm finds itoptimal to attract an employee of certain type with positive probability, changing the parametervalues would not drive this probability down to 0.

22

ployee’s independent development capabilities, α f and αe. The following Proposi-tion characterizes these comparative statics.

Proposition 6 Let L∗(γ, α f , αe) ≥ max{Lmins (v, βH), Lmin

c (v, βH)}. Then, the firm’soptimal level of support for exploration is increasing in γ and α f and decreasing in αe.

An improvement in the firm’s outside option in the negotiation subgame, ei-ther through an increase γ or α f , has two effects. First, it increases the firm’s sur-plus from internally explored ideas, which induces the firm to increase its support.Second, it diminishes the employee’s willingness to explore ideas within the firmdue to a reduction in his expected downstream payoff — a negative retention ef-fect. To mitigate the employee’s reduced incentive to explore internally, the firmfurther increases its level of support. In contrast, an improvement in the outsideoption of the employee, through an increase in αe, decreases both the firm’s surplusfrom internal exploration, as well as the employee’s incentive to explore externally,whereby the firm reduces its support.

In addition to examining how the above policy and market parameters im-pact the level of support offered by the firm, we are also interested in their im-pact on the firm’s profitability, particularly since some of their variability may bedirectly linked to the firm’s organizational structure and policies. For instance,closely monitoring an employee’s exploration efforts can reduce the cost of repli-cating emerging ideas, thereby increasing γ and α f and strengthening the firm’sposition in negotiations. Similarly, a more hierarchical organizational structurecan strengthen the firm’s relative bargaining power, while a flatter structure canprovide employees with more autonomy.

Note that in absence of a retention effect, the firm’s profit is always increasingas its downstream bargaining position improves, since an increase in γ, α f , and/ora decrease in αe all increase the firm’s surplus for every level of support L. How-ever, strengthening the firm’s bargaining position also has an indirect effect on theability of the firm to retain ideas in-house. In particular, all else being equal, higherγ and α f reduce the employee’s incentive for internal exploration and widen theregion of ideas that will be taken outside the firm, (∆I

s(L, v, β, θ∗I ), ∆Ic(L, v, β, θ∗I )).

Consequently, it becomes increasingly costly for the firm to provide sufficient re-tention incentives for the employee. Thus, the retention effect tends to reduce thefirm’s profit. Interestingly, the negative impact of the retention effect on the firm’sprofit may dominate, as the following example illustrates.

23

0 0.2 0.4 0.6 0.8 10

5

10

15

γ

L*

L*

Lmin(βH

)

Lmin(βL)

(a) Optimal support as a function of γ

0 0.2 0.4 0.6 0.8 11.5

2

2.5

3

3.5

4

γ

Π*

(b) Expected profit as a function of γ

0 0.1 0.2 0.3 0.4 0.5 0.60

1

2

3

4

5

6

αf

L*

L*

Lmin(βH

)

Lmin(βL)

(c) Optimal support as a function of α f

0 0.1 0.2 0.3 0.4 0.5 0.60.5

1

1.5

2

2.5

3

αf

Π*

(d) Expected profit as a function of α f

0 0.1 0.2 0.3 0.4 0.50

2

4

6

8

αe

L*

L*

Lmin(βH

)

Lmin(βL)

(e) Optimal support as a function of αe

0 0.1 0.2 0.3 0.4 0.5

2.45

2.5

2.55

2.6

2.65

αe

Π*

(f) Expected profit as a function of αe

Figure 3: Firm’s optimal support and expected profit as functions of γ, α f , and αe.

Example 2 Consider the parameter values specified in Example 1. Let Lmin(β) = max{Lmin

s (v, β), Lminc (v, β)}. Figure 3 illustrates the effect of increasing γ , α f and αe on

the optimal level of support and on the firm’s profitability for the case in which both typesare attracted with positive probability for both complementary and substitute ideas, i.e.L∗(γ, α f , αe) ≥ Lmin(β) for all β. In this case, L∗(γ, α f , αe) is continuously increasing inγ and α f and continuously decreasing in αe, but the firm’s optimal profit is non-monotonicin these variables.

Example 2 illustrates that a firm may wish to willingly surrender some of itscontrol over employees’ innovations in order to retain ideas in-house. This findingcan help explain why certain innovation-focused institutions, such as academia,

24

have adopted a flat organizational structure, giving employees significant auton-omy and control over their ideas.

It is also important to point out that while a weaker bargaining position vis-a-vis the employee may be ex-ante optimal for the firm, it is not ex-post incentivecompatible. In the absence of credible commitment mechanisms, a firm wouldhave incentives to improve its bargaining position once it gains access to innova-tions. This observation highlights the importance of well-specified and enforce-able mechanisms, such as a well functioning legal system to govern the allocationof property rights and market competition. It further suggests that laws strength-ening firms’ claims over ideas emerging from their employees might actually hurtprofitability by making it more difficult to induce internal exploration.

In the remainder of this subsection, we briefly examine the possibility that thefirm may choose not to attract internal exploration of some ideas by high-type em-ployees. The following example modifies Example 2 by reducing the prior likeli-hood that an employee is a high type. This makes it less profitable to incentivizeinternal exploration by high types, which can cause the firm to discontinuouslyreduce its level of support for high values of γ and α f .

Example 3 The parameter values are the same as in Example 2, except θ = 0.3. Fig-ures 4(a) and 4(b) plot the optimal level of support L∗ as γ and α f vary. As the figuresillustrate, L∗(γ, α f , αe) ≥ Lmin(βH) does not hold for very high values of γ and/or α f .Instead, the firm chooses to reduce its level of support below the threshold required to attractcomplementary ideas by high types.

Example 3 illustrates that for high values of γ and α f , the optimal level of sup-port exhibits a downward jump. This jump is due to the fact that it becomes in-creasingly costly to induce internal exploration of complementary ideas by high-type employees. Thus, the global maximum switches from the local maximum thatretains both complementary and substitute ideas by high-type employees (withpositive probability) to the local maximum under which only substitute ideas byhigh-type employees are possibly retained. As mentioned previously, low-typeemployees always choose to remain with the firm. This example illustrates thatwhile the level of exploration support is locally increasing in the firm’s bargainingposition, there may exist a point at which it becomes too costly for the firm to in-duce high-type employees to explore internally. Consequently, the firm “gives up”on bringing in some of their ideas and discontinuously reduces its level of support.

25

0 0.2 0.4 0.6 0.8 10

5

10

15

γL

*

L*

Lmin(βH

)

Lmin(βH

)

(a) Optimal support as a function of γ

0 0.1 0.2 0.3 0.4 0.5 0.60

1

2

3

4

5

αf

L*

L*

Lmin(βH

)

Lmin(βL)

(b) Optimal support as a function of α f

Figure 4: The firm’s chosen level of support as functions of γ and α f .

5 Conclusions

We show that employees who leave their employment to pursue new venturestend to develop products that are weakly related to their former employers’ linesof business. While increasing the level of support for innovation can induce the in-ternal exploration of a wider range of ideas, we find that such policies may also in-crease employee turnover in downstream development stages. Hence, consistentwith anecdotal evidence, our findings suggest that firms with generous policiesfor supporting innovation are also likely to have a significant number of employ-ees leaving to form new ventures.

When choosing its optimal level of support, the firm in our model balancesthe benefits of inducing higher levels of exploration in-house with the cost of sup-porting this exploration activity. We showed that as the firm’s relative bargainingposition vis-a-vis an employee strengthens, its chosen level of support is likely toincrease, but its ex-ante expected profits may decrease. This suggests that the firmis likely to favor policies that enable employees to retain some control over theirinternally explored ideas. Policies of this sort can include a flatter organizationalstructure and a balanced allocation of property rights between the firm and its

26

employees.Future work can incorporate a mechanism-design framework, where the firm

is able to structure roles for employees in order to make the discovery of certain in-novations more likely (e.g., innovations that are more complementary to the firm’sexisting line of products). Another direction is to consider the firm’s incentivesfor committing ex ante to a development strategy in order to affect the employee’sexploration choice. One may also consider a competitive landscape where outsideinvestors, as well as other firms, are competing for attracting new ideas and theirdevelopment by the firm’s employees, and a framework where employees choosea subset of ideas to pursue from a larger set of ideas.

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29

Appendix

Proof of Proposition 1. We consider the case of vi = 0 and vi = v separately.

1. Let vi = 0. Then, the employee’s outside option is common knowledge and

equal to πEe = 0. Thus, disagreements do not arise in equilibrium and the efficient

outcome is implemented. Joint development of the idea is efficient if and only if

π J = max{g∆, 0} ≥ max{∆, 0} + w = πof + w or ∆ > w

gc−1 > 0. In this case, if

negotiations favor the firm, then it makes an offer of w. Otherwise, if negotiations

favor the employee, then he makes an offer of πof . For ∆ ∈

(0, w

gc−1

], the efficient

outcome is for the firm to develop independently and for the employee to focus

on the core task resulting in ∆ for the firm and w for the employee. For ∆ ≤ 0,

the efficient outcome is shelving resulting in payoffs of 0 for the firm and w for the

employee.

2. Next, we consider the case of vi = v. The employee makes a take-it-or-leave-it

offer of πof with probability (1− γ), which is subsequently accepted by the firm.

If, instead, negotiations favor the firm, occurring with probability γ, the firm has

two options:

i) Offer βHαev, which is accepted with probability 1, resulting in an expected

payoff of π J − βHαev for the firm; or ii) Offer βLαev, which is accepted with prob-

ability θI , resulting in an expected payoff of (1− θI)(πJ − βLαev) + θIπ

of for the

firm. It is optimal for the firm to offer βHαev if and only if its expected payoff from

doing so exceeds its expected payoff from offering βLαev. That is,

π J ≥ πof + βLαev +

(βH − βL) αevθI

(A-1)

For ∆ ≥ 0, it is straightforward to check that the above inequality is satis-

fied if and only if ∆ ≥ θI(α f +βLαe−1)+(βH−βL)αe

θI(gc−1) v. Then, we can define ∆dc (v, θI) ≡

max{

θI(α f +βLαe−1)+(βH−βL)αe

θI(gc−1) v, 0}

. Clearly, ∆dc (v, θI) is non-increasing in θI . Fur-

ther, ∆dc (v, θI) > 0 if and only if θI <

(βH−βL)αe1−α f−βLαe

.

For ∆ ≤ 0, there are two cases to consider:

30

• ∆ ≥ − 1gs

v, in which case equation A-1 is satisfied if and only if

∆ ≤ −θI(α f + βLαe − 1) + (βH − βL) αe

θI(1− gs)v ≡ ∆1(v, θI).

• ∆ < − 1gs

v, in which case equation A-1 is satisfied if and only if

∆ ≤ −θI(α f + βLαe

)+ (βH − βL) αe

θIv ≡ ∆2(v, θI).

Combining the above inequalities, it can be verified that given ∆ < 0, equa-

tion A-1 is satisfied for ∆ ≤ max {∆1(v, θI), ∆2(v, θI)}. Therefore, ∆ds (v, θI) ≡

min {max {∆1(v, θI), ∆2(v, θI)} , 0}. It can be readily verified that ∆ds (v, θI) is non-

decreasing in θI and that ∆ds (v, θI) < 0 if and only if θI <

(βH−βL)αe1−α f−βLαe

.

Proof of Corollary 1. We consider vi = 0 and vi = v separately.

1. Consider vi = 0. From the proof of Proposition 1, we know that joint devel-

opment takes place if ∆ > wgc−1 . In this case, the firm makes a take-it-or-leave-it

offer of w to the employee with probability γ and the employee makes a take-it-or-

leave-it offer to the firm of πof with probability (1− γ). For ∆ ≤ w

gc−1 , the employee

focuses on the core task and the firm develops independently whenever optimal.

Therefore,

πNe (0, ∆, β, θI) =

w i f ∆ ≤ wgc−1

γw + (1− γ)(π J − πof ) i f ∆ > w

gc−1

(A-2)

πNf (0, ∆, θI) =

max{0, ∆} i f ∆ ≤ wgc−1

γ(π J − w) + (1− γ)πof i f ∆ > w

gc−1

(A-3)

Therefore, dπNe (0,∆,β,θI)

d∆ = 0 for ∆ ≤ wgc−1 and dπN

e (0,∆,β,θI)d∆ = (1− γ)(gc − 1) > 0

31

for ∆ > wgc−1 . For the firm,

dπNf (0,∆,θI)

d∆ = 0 for ∆ ≤ 0, and

dπNf (0, ∆, θI)

d∆=

1 i f ∆ ∈(

0, wgc−1

]γgc + (1− γ) i f ∆ > w

gc−1

> 0

2. Consider vi = v. In this case, the employee has a credible option of developing

independently resulting in πoe , while the firm’s outside option is πo

f . In the agree-

ment region ∆ /∈ (∆ds (v), ∆d

c (v)), the firm makes a take-it-or-leave-it offer of βHαev,

which is accepted with probability 1 by the employee. In the disagreement region,

∆ ∈ (∆ds (v), ∆d

c (v)), the firm makes a take-it-or-leave-it offer of βLαev, which is

accepted by the low type and rejected by the high type. Let πoe be defined as

πoe (v, βH) = αeβHv (A-4)

πoe (v, βL) =

βHαev i f ∆ 6∈ (∆ds (v, θI), ∆d

c (v, θI))

βLαev i f otherwise(A-5)

Then the employee’s expected payoff from the negotiation stage is given by

πNe (v, ∆, β, θI) = γπo

e + (1− γ)(π J − πof ) (A-6)

Thus,

dπNe (v, ∆, β, θI)

d∆=

−(1− γ)(1− gs) i f ∆ < 0

(1− γ)(gc − 1) i f ∆ > 0

The firm’s expected payoff is given by

πNf (v, ∆, θI) =

(1− γ)πof + γ(π J − βHαev) if ∆ 6∈ (∆d

s , ∆dc )

(1− γ)πof + γ[θIπ

of + (1− θI)(π

J − βLαev)] otherwise

Since both πof and π J are increasing in ∆, it follows that

dπNf (v,∆,θI)

d∆ > 0.

Proof of Proposition 2. Consider vi = 0. From the proof of Corollary 1, the

32

employee’s expected payoff from internal exploration is given by

π Ie =

0 if ∆ ≤ wgc−1

p(L)[πNe (0, ∆, β, θI)− w] + w if ∆ > w

gc−1

The employee’s payoff from focusing on his core task is πDe = w, and his payoff

from external exploration is πEe = 0. Given that πN

e (0, ∆, β, θI) > w for ∆ > wgc−1 ,

the result follows immediately.

Proof of Proposition 3. Consider vi = v. The employee’s payoff from internal

exploration is π Ie = p(L)[πN

e (v, ∆, β, θI) − w] + w, where πNe (v, ∆, β, θI) is given

by (A-6). Since πNe (v, ∆, β, θI) > w, payoff from internal exploration exceeds the

payoff from pursuing the core task and the employee chooses between internal

and external exploration. Moreover, from the proof of Corollary 1, we have

dπNe (v, ∆, β, θI)

d∆=

−(1− γ)(1− gs) i f ∆ < 0

(1− γ)(gc − 1) i f ∆ > 0

Thus, dπ Ie

d∆ < 0 for ∆ < 0 and dπ Ie

d∆ > 0 for ∆ > 0. Then, if π Ie(v, 0, β, θI , L) ≥ πE

e (v, β),

the payoff from internal exploration always exceeds the payoff from external ex-

ploration, and ∆Is = ∆I

c = 0. Otherwise, ∆Is and ∆I

c are defined as the solu-

tions of equation (2). Note that since dπ Ie

d∆ < 0 for ∆ < 0, ∆Is is unique and

π Ie(v, ∆, β, θI , L) > πE

e (v, β) for ∆ < ∆Is . By the same token, since dπ I

ed∆ > 0 for

∆ > 0, ∆Ic is unique and π I

e(v, ∆, β, θI , L) > πEe (v, β) for ∆ > ∆I

c.

To establish Properties 1 and 2, let ∆Ij 6= 0. It then follows that D(v, ∆I

j , β, θI , L) ≡π I

e(v, ∆Ij , β, θI , L)− πE

e (v, β) = 0. Then, by Implicit Function theorem, we have

d∆Ij /dL = − p′(L)(πN

e −w)

p(L)∂πNe /∂∆

. The numerator is positive due to p′(L) > 0 and πNe > w.

The denominator is positive for complements and negative for substitutes. There-

fore, d∆Is

dL > 0 and d∆Ic

dL < 0.

For Properties 3 and 4, note that πNe (v, ∆, βH), as given by equation (A-6), is not a

33

function of θI , establishing Property 3. To establish Property 4, recall from Propo-

sition 1 that ∆ds (v, θI) (∆d

c (v, θI)) is increasing (decreasing) in θI . This implies thatd∆I

s(L,v,βL,θI)dθI

= − p(L)∂πNe /∂θI

p(L)∂πNe /∂∆

≥(≤)0 for substitutes (complements).

For Properties 5 and 6, note that D(v, ∆, β, θI , L) = 0 can be written as

p(L)(1− γ)(π J − πof ) + (1− p(L))w = poβv− p(L)γπo

e (v, β)

where πoe (v, β) is defined by equations (A-4) and (A-5). Note that for poβv ≤

p(L)γπoe (v, β), ∆I

j (L, v, β, θI) = 0. Therefore, we consider the case of poβv >

p(L)γπoe (v, β) for at least one of the types. In this case, it is sufficient to show that

the right-hand side is increasing in β. This is straightforward to establish since

βH(po − p(L)γαe)v > βL(po − p(L)γαe)v.

Proof of Proposition 4. By Proposition 3, we have that ∆Ij (L, v, βH) is indepen-

dent of θI . We also have that ∆c(L, v, βL, θI) ≤ ∆c(L, v, βH) and ∆s(L, v, βL, θI) ≥∆s(L, v, βH) for all θI . This implies that both employee types choose internal ex-

ploration for ∆ /∈ (∆Is(L, v, βH), ∆I

c(L, v, βH)). By Bayes’ Rule, this implies that the

equilibrium belief is θ∗I = θ. For ∆ ∈ (∆Is(L, v, βH), ∆I

c(L, v, βH)) the high type al-

ways explores externally. Thus, the low type is the only one that may have strict

incentives to explore inside the firm.

Given θI = 0, the low type would choose internal exploration provided ∆ /∈(∆I

s(L, v, βL, 0), ∆Ic(L, v, βL, 0)). By Proposition 3, ∆I

s(L, v, βL, θI) is non-decreasing

in θI and ∆Ic(L, v, βL, θI) is non-increasing in θI , indicating that the incentives for in-

ternal exploration are weakly increasing in θI . Therefore, θ∗I = 0 is the unique equi-

librium belief that can be supported over regions ∆ ∈ (∆Is(L, v, βH), ∆I

s(L, v, βL, 0)]

and ∆ ∈ [∆Ic(L, v, βL, 0), ∆I

c(L, v, βH)).

For ∆ ∈ (∆Is(L, v, βL, 0), ∆I

c(L, v, βL, 0)), the only possible equilibrium is for both

types to explore externally. To see this, note that any belief θI that results in internal

exploration by the low type in the region ∆ 6∈ (∆s(L, v, βL, θI), ∆c(L, v, βL, θI)) can-

not be supported as an equilibrium — in equilibrium, Bayes’ Rule requires θI = 0,

34

a contradiction. An off-equilibrium belief θ∗I = 0 in this region guarantees no de-

viation incentives by the low type.

Proof of Proposition 5. Let F(·|vi) denote the conditional distribution of ∆ for a

given realization of vi. Then the probability of internal exploration is given by

P(L) =

[(1− ψ)

(1− F

(w

gc − 1

∣∣∣∣ 0))]

+

+ψ ∑β

Pr(β)[1−

(F(∆I

c(L, v, β, θ∗I )|v)− F(∆∗s (L, v, β, θ∗I )|v))]

.

From Proposition 3, ∂∆Is(L,v,β,θ∗I )

∂L ≥ 0 and ∂∆Ic(L,v,β,θ∗I )

∂L ≤ 0. Thus,

dPdL

= ψ ∑β

Pr (β)

[f (∆I

s |v)∂∆I

s∂L− f (∆I

c|v)∂∆I

c∂L

]≥ 0

Next, we consider the likelihood of downstream disagreements. Note that a

necessary condition for disagreements to take place is ∆ /∈ (∆Is(L, v, βH), ∆I

c(L, v, βH))

since otherwise the high type explores externally and the negotiations never fail.

By Proposition 4, θ∗I = θ in this region. Proposition 1 then implies that downstream

disagreements are not possible for θ∗I = θ ≥ (βH−βL)αe1−α f−βLαe

since it then holds that

∆ds (v, θ∗I ) = ∆d

c (v, θ∗I ) = 0. For θ∗I = θ < (βH−βL)αe1−α f−βLαe

, ∆ds (v, θ) < 0 and ∆d

c (v, θ) > 0.

Downstream disagreements occur if and only if ∆ ∈ (∆ds (v, θ), ∆I

s(L, v, βH, θ)) ∪(∆I

c(L, v, βH, θ), ∆dc (v, θ)). By Proposition 3, ∆I

s(L, v, βH) is increasing in L and

∆Ic(L, v, βH) is decreasing in L. Therefore, there exists L ≥ 0 such that the region of

downstream disagreements is non-empty and increasing in L.

Proof of Lemma 1. The proof for complements and substitutes is analogous; we

show the case of complements, ∆ ≥ 0.

For ∆ ≥ 0, π Ie(v, ∆, θI , L) is strictly increasing in L and ∆. Lmin

c (v, β) is defined

as the smallest level of exploration support L such that π Ie(v, ∆, θI , L) ≥ πE

e (v, β).

Similarly, Lmaxc (v, β) is defined as the smallest level of L such that π I

e(v, 0, θI , L) ≥πE

e (vi, β). Clearly, Lmaxc (v, β) ≥ Lmin

c (v, β) since π Ie(v, ∆, θI , L) is increasing in L

35

and ∆ for ∆ ≥ 0. For Lminc (v, β) = 0 and Lmax

c (v, β) = 0, Properties 2 and 3 trivially

hold. Therefore, we focus on Lminc (v, β) > 0 and Lmax

c (v, β) > 0, where Lminc (v, β)

is the solution of

π Ie(vi, ∆, θI , Lmin

c ) = πEe (vi, β), (A-7)

and Lmaxc (v, β) is the solution of

π Ie(vi, 0, θI , Lmax

c ) = πEe (vi, β). (A-8)

To see that Lminc (v, βH) ≥ Lmin

c (v, βL), note that equation (A-7) can be rewritten as

p(Lminc )[γπo

e (v, β) + (1− γ)(gc∆ + v− ∆− α f v)− w] + w− poβv = 0

where πoe (v, β) is defined by equations (A-4) and (A-5). Note that the left-hand

side is increasing in L since γπoe + (1− γ)(gc∆ + v− ∆− α f v) > w and p′(L) >

0. Moreover, p(Lminc )γπo

e (v, β) − poβv < 0; otherwise the left-hand side will be

strictly greater than 0. This implies that the left-hand side is decreasing in β, since

0 > p(L)γπoe (v, βL)− poβLv > p(L)γπo

e (v, βH)− poβHv holds for L ≤ Lminc (v, βH).

It follows that Lminc (v, βH) > Lmin

c (v, βL). To show that Lmaxc (v, βH) ≥ Lmax

c (v, βL),

note that equation (A-8) can be rewritten as

p(Lmaxc )[γπo

e (v, β) + (1− γ)(1− α f )v− w] + w− poβv = 0

Using an argument analogous to the case of Lminc (v, β), it can be readily shown that

Lmaxc (v, βH) ≥ Lmax

c (v, βL).

Proof of Proposition 6. Consider L∗(γ, αe, α f ) > max{Lmins (v, β), Lmin

c (v, β)}.Then, L∗(γ, αe, α f ) is defined as the solution of

∂Π f (L∗)∂L = 0, where

∂Π f (L)∂L is defined

by equation (4). By Implicit function theorem, it is sufficient to establish∂Π f (L∗)

∂L∂γ >

0,∂Π f (L∗)

∂L∂α f> 0 and

∂Π f (L∗)∂L∂αe

< 0. Let x ∈ {γ, α f , αe}. Then,

36

∂Π f (L)∂L∂x

= E

[∂S f (vi, ∆, β, L)

∂L∂x

∣∣∣∣∆ /∈(

∆Is , ∆I

c

)]+

+ψE

[∂S f

(v, ∆I

s , β, L)

∂xf (∆I

s |v)∂∆I

s∂L− ∂S f

(v, ∆I

c, β, L)

∂xf (∆I

c|v)∂∆I

c∂L

∣∣∣∣∣ v

]+

+ψE

[d[S f

(v, ∆I

s , β, L)

f (∆Is |v)]

dL∂∆I

s∂x

∂∆Is

∂L+ S f (v, ∆I

s , β, L) f (∆Is |v)

∂2∆Is

∂L∂x

∣∣∣∣∣ v

]−

−ψE

[d[S f

(v, ∆I

c, β, L)

f (∆Ic|v)]

dL∂∆I

c∂x

∂∆Ic

∂L− S f (v, ∆I

c, β, L) f (∆Ic|v)

∂2∆Ic

∂L∂x

∣∣∣∣∣ v

]

Recall from Proposition 3 that ∂∆Is

∂L ≥ 0 and ∂∆Ic

∂L ≤ 0. Given Assumption 1,d[S f

(v,∆I

j ,β,L)

f (v,∆Ij ,β,L|v)]

dL ≤ 0 for j = {s, c}. We proceed in sequence to establish the

signs of the remaining variables:

• ∂S f (vi,∆,β,L)∂L∂x = p′(L)

∂πNf (vi,∆,β,θ∗I )

∂x , where it can be readily established that∂πN

f (vi,∆,β,θ∗I )∂γ > 0,

∂πNf (vi,∆,β,θ∗I )

∂α f> 0 and

∂πNf (vi,∆,β,θ∗I )

∂αe < 0

•∂S f

(v,∆I

j ,β,L)

∂x = p(L)∂πN

f (vi,∆,β,θ∗I )∂x .

• ∂∆Ij

∂x = − ∂D/∂x∂D/∂∆ for ∆I

s ∈ [∆, 0) and ∆Ic ∈ [0, ∆) where D(v, ∆, β, θ∗I , L) ≡

π Ie(v, ∆, β, θ∗I , L)− πE

e (v, β). Given π Ie(v, ∆, β, θ∗I , L) = p(L)(πN

e (v, ∆, β, θ∗I )−w) + w, we have

∂∆Ij

∂x = − ∂πNe /∂x

∂πNe /∂∆

. It is straightforward to establish that∂πN

e (v,∆,β,θ∗I )∂γ < 0, ∂πN

e (v,∆,β,θ∗I )∂α f

< 0 and ∂πNe (v,∆,β,θ∗I )

∂αe > 0. Moreover, from Corol-

lary 1, ∂πNe (v,∆,β,θ∗I )

∂∆ > 0 for complements and ∂πNe (v,∆,β,θ∗I )

∂∆ < 0 for substitutes.

Therefore, ∂∆Ic

∂γ > 0,∂∆Is

∂γ < 0, ∂∆Ic

∂α f> 0,∂∆I

s∂α f

< 0, ∂∆Ic

∂αe< 0, and ∂∆I

s∂αe

> 0.

• ∂∆Ij

∂L∂x =∂∆I

j∂x∂L = ∂

∂L

[− ∂πN

e /∂x∂πN

e /∂∆

]= 0, since πN

e is not a function of L.

Given the signs of the variables above, it is straightforward to establish that∂Π f (L∗)

∂L∂γ > 0,∂Π f (L∗)

∂L∂α f> 0, and

∂Π f (L∗)∂L∂αe

< 0.

37

Notation Table

e research employeef firmw competitive wage

vi ∈ {0, v} stand alone valuation of the idea∆ externality imposed by the ideaψ probability that vi = v

β ∈ {βH, βL} employee’s entrepreneurial abilityθ firm’s prior belief that β = βH

g ∈ {gc, gs} synergies from joint developmentαe, α f profit eroding effect of competition

γ probability that firm makes an offer in negotiation stageE, R employee’s choice: External exploration vs. Remain with firm

{D, I} ∈ R employee’s choice given R: Drop the idea vs. Internal explorationpo likelihood of successful exploration if idea is pursued outside the firmL level of exploration support offered by the firm

p(L) likelihood of successful exploration if idea is pursued inside the firmπD

e employee’s payoff from dropping the ideaπ J(.) surplus from internal (joint) handling of an explored idea

πEe (.), πE

f (.) expected payoffs from external explorationπ I

e(.), π If (.) expected payoffs from internal exploration

πoe (.), πo

f (.) expected payoffs from independent development after internal explo-ration

Table 1: A summary of the notation.

38